[hcta]

surely being able to construct a turing-complete computing device is a sufficient condition to qualify as general intelligence, and it seems like a reasonable bar for considering a purported intelligent agent as interesting.

> It seems foolish to me to search for something when we can't even define it.

This is backwards. The vast majority of concepts outside mathematics are pretty hard to rigorously define. The way we approach the problem of trying to find a sensible definition is by searching for examples and counterexamples and performing induction.